Compressible Flow Free Textbook

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Oblique Shock Examples

$\begin{examl} Air flows at Mach number ($M_1$) or $M_x= 4$ is approaching a wed... ... the weak, the strong Mach numbers, and the respective shock angles. \end{examl}$
Solution

The find maximum wedge angle for (

)

has to be equal to zero. The wedge angle that satisfies this requirement by equation (13.28) is the solution (a side to the case proximity of $\delta = 0$ ). The maximum values are:

$\rule[-0.1in]{0.pt}{0.3 in}\mathbf{M_x}$	$\mathbf{M_y}$	$\mathbf{\delta_{max}}$	$\mathbf{\theta_{max}}$
4.0000	0.97234	38.7738	66.0407

To obtain the results of the weak and the strong solutions, utilize either equation (13.28) or the Potto-GDC, which yields the following results:

$\rule[-0.1in]{0.pt}{0.3 in}\mathbf{M_x}$	$\mathbf{{M_y}_s}$	$\mathbf{{M_y}_w}$	$\mathbf{\theta_s}$	$\mathbf{\theta_w}$	$\mathbf{\delta }$
4.0000	0.48523	2.5686	1.4635	0.56660	0.34907

**Figure:** Oblique shock occurs around a cone. This photo is courtesy of Dr. Grigory Toker, a Research Professor at Cuernavaco University of Mexico. According to his measurement, the cone half angle is $15^\circ$ and the Mach number is 2.2.

$\begin{examl} A cone shown in Figure \eqref{oblique:fig:sharpNose} is exposed to... ...s the photo taken based on the assumption that the cone is a wedge. \end{examl}$
Solution

The measurement shows that cone angle is $14.43^\circ$ and shock angle is $30.099^\circ$ . With given two angle the solution can be obtained utilizing equation (13.59) or the Potto-GDC.

$\rule[-0.1in]{0.pt}{0.3 in} \mathbf{M_1}$	$\mathbf{{M_y}_s}$	$\mathbf{{M_y}_w}$	$\mathbf{\theta_s}$	$\mathbf{\theta_w}$	$\mathbf{\delta }$	$\mathbf{{P_0}_y \over {P_0}_x }$
3.2318	0.56543	2.4522	71.0143	30.0990	14.4300	0.88737

Because the flow is around Cone it must be a weak shock. Even if the cone was a wedge, the shock will be weak because the maximum (transition to a strong shock) occurs at about $60^{\circ}$ . Note that Mach number is larger than the predicted by the wedge.

**Figure:** $\;$ Maximum values of the properties in an oblique shock
$\begin{figure}\centerline{\includegraphics {calculations/figures/obliqueMax}} \end{figure}$

**Figure:** Two variations of inlet suction for supersonic flow.
$\begin{figure}\centerline{\includegraphics {cont/oblique/inletSuction}} \end{figure}$

Next: Application of Oblique Shock Up: Detached Shock Previous: Issues Related to the Index

Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21